Polynomially Bounded Matrix Interpretations

Abstract

Matrix interpretations can be used to bound the derivational complexity of rewrite systems. We present a criterion that completely characterizes matrix interpretations that are polynomially bounded. It includes the method of upper triangular interpretations as a special case, and we prove that the inclusion is strict. The criterion can be expressed as a finite domain constraint system.
It translates to a Boolean constraint system with a size that is polynomial in the dimension of the interpretation. We report on performance of an implementation.